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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

A note on diophantine equation $ Y\sp{2}+k=X\sp{5}$


Author: Josef Blass
Journal: Math. Comp. 30 (1976), 638-640
MSC: Primary 10B15
MathSciNet review: 0401638
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Abstract: We show that if the class number of the quadratic field $ A(\sqrt { - k} )$ is not divisible by 5, and if k is not congruent to 7 modulo 8, then the equation $ {Y^2} + k = {X^5}$ has no solutions in rational integers X, Y with the exception of $ k = 1,19,341$.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1976-0401638-2
PII: S 0025-5718(1976)0401638-2
Article copyright: © Copyright 1976 American Mathematical Society